scholarly journals Global Convergence of a Modified LS Method

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Liu JinKui ◽  
Du Xianglin
Keyword(s):  
Global Convergence ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Uniformly Convex ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search

The LS method is one of the effective conjugate gradient methods in solving the unconstrained optimization problems. The paper presents a modified LS method on the basis of the famous LS method and proves the strong global convergence for the uniformly convex functions and the global convergence for general functions under the strong Wolfe line search. The numerical experiments show that the modified LS method is very effective in practice.

scholarly journals Some generalized three-term conjugate gradient methods based on CD approach for unconstrained optimization problems

2021 ◽  
Vol 3 (2) ◽  
pp. 67-82
Author(s):  
Ladan Arman ◽  
Yuanming Xu ◽  
Long Liping
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search

Abstract In this paper, based on the efficient Conjugate Descent (CD) method, two generalized CD algorithms are proposed to solve the unconstrained optimization problems. These methods are three-term conjugate gradient methods which the generated directions by using the conjugate gradient parameters and independent of the line search satisfy in the sufficient descent condition. Furthermore, under the strong Wolfe line search, the global convergence of the proposed methods are proved. Also, the preliminary numerical results on the CUTEst collection are presented to show effectiveness of our methods.

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
Author(s):  
Ping Hu ◽  
Zong-yao Wang
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Combination ◽  
Combination Rule ◽  
Combination Technique ◽  
Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

scholarly journals A Truncated Descent HS Conjugate Gradient Method and Its Global Convergence

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Wanyou Cheng ◽  
Zongguo Zhang
Keyword(s):  
Global Convergence ◽  
Line Search ◽  
Optimization Problems ◽  
Test Problems ◽  
Uniformly Convex ◽  
Convex Problems ◽  
Unconstrained Optimization Problems ◽  
Globally Convergent ◽  
Armijo Line Search ◽  
Numerical Performance

Recently, Zhang (2006) proposed a three-term modified HS (TTHS) method for unconstrained optimization problems. An attractive property of the TTHS method is that the direction generated by the method is always descent. This property is independent of the line search used. In order to obtain the global convergence of the TTHS method, Zhang proposed a truncated TTHS method. A drawback is that the numerical performance of the truncated TTHS method is not ideal. In this paper, we prove that the TTHS method with standard Armijo line search is globally convergent for uniformly convex problems. Moreover, we propose a new truncated TTHS method. Under suitable conditions, global convergence is obtained for the proposed method. Extensive numerical experiment show that the proposed method is very efficient for the test problems from the CUTE Library.

scholarly journals A modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems

2017 ◽  
Vol 7 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Pro Kaelo ◽  
Sindhu Narayanan ◽  
M.V. Thuto
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid method.

Global convergence of a modified Fletcher–Reeves conjugate gradient method with Wolfe line search

2019 ◽  
Vol 13 (04) ◽  
pp. 2050081
Author(s):  
Badreddine Sellami ◽  
Mohamed Chiheb Eddine Sellami
Keyword(s):  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradients ◽  
Gradient Algorithm ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search

In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. we propose a modified Fletcher–Reeves (abbreviated FR) [Function minimization by conjugate gradients, Comput. J. 7 (1964) 149–154] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter [Formula: see text] is proposed. The parameter [Formula: see text] is computed by means of the conjugacy condition, thus an algorithm which is a positive multiplicative modification of the Hestenes and Stiefel (abbreviated HS) [Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sec. B 48 (1952) 409–436] algorithm is obtained, which produces a descent search direction at every iteration that the line search satisfies the Wolfe conditions. Under appropriate conditions, we show that the modified FR method with the strong Wolfe line search is globally convergent of uniformly convex functions. We also present extensive preliminary numerical experiments to show the efficiency of the proposed method.

scholarly journals Nonlinear Conjugate Gradient Methods with Wolfe Type Line Search

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yuan-Yuan Chen ◽  
Shou-Qiang Du
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Convergence Results ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

Nonlinear conjugate gradient method is one of the useful methods for unconstrained optimization problems. In this paper, we consider three kinds of nonlinear conjugate gradient methods with Wolfe type line search for unstrained optimization problems. Under some mild assumptions, the global convergence results of the given methods are proposed. The numerical results show that the nonlinear conjugate gradient methods with Wolfe type line search are efficient for some unconstrained optimization problems.

New hyrid conjugate gradient method as a convex combination of HZ and CD methods

2021 ◽  
pp. 2150187
Author(s):  
Amira Hamdi ◽  
Badreddine Sellami ◽  
Mohammed Belloufi
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Convex Combination ◽  
Gradient Algorithm ◽  
Unconstrained Optimization Problems ◽  
Gradient Parameter ◽  
Sufficient Descent ◽  
Wolfe Line Search

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems, the conjugate gradient parameter [Formula: see text] is computed as a convex combination of [Formula: see text] and [Formula: see text]. Under the wolfe line search, we prove the sufficient descent and the global convergence. Numerical results are reported to show the effectiveness of our procedure.

scholarly journals A COMPARATIVE STUDY OF SOME MODIFICATIONS OF CG METHODS UNDER EXACT LINE SEARCH

2020 ◽  
Vol 1 (1) ◽  
pp. 12-17
Author(s):  
Yasir Salih ◽  
Mustafa Mamat ◽  
Sukono Sukono
Keyword(s):  
Conjugate Gradient ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Test Problems ◽  
Convergence Properties ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Unconstrained Optimization

Conjugate Gradient (CG) method is a technique used in solving nonlinear unconstrained optimization problems. In this paper, we analysed the performance of two modifications and compared the results with the classical conjugate gradient methods of. These proposed methods possesse global convergence properties for general functions using exact line search. Numerical experiments show that the two modifications are more efficient for the test problems compared to classical CG coefficients.

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